Daily O-D Matrix Estimation using Cellular Probe Data

Transcription

1 Zhang, Qn, Dong and Ran Daly O-D Matrx Estmaton usng Cellular Probe Data 0 0 Y Zhang* Department of Cvl and Envronmental Engneerng, Unversty of Wsconsn-Madson, Madson, WI 0 Phone: -0-- E-mal: zhang@wsc.edu Xao Qn Department of Cvl and Envronmental Engneerng, South Daota State Unversty Broongs, SD 00 Phone: -0-- E-mal: xqn@cae.wsc.edu Shen Dong Department of Cvl and Envronmental Engneerng, Unversty of Wsconsn-Madson, Madson, WI 0 Phone: -0-- E-mal: sdong@wsc.edu Bn Ran Department of Cvl and Envronmental Engneerng, Unversty of Wsconsn-Madson, Madson, WI 0 Phone: E-mal: bran@wsc.edu * Correspondng Author TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

2 0 Zhang, Qn, Dong and Ran ABSTRACT Wth the fast-growng wreless-communcaton maret, the cellular postonng technologes are becomng one of the mportant means to montorng real-tme traffc status, provdng traveler nformaton, measurng system operatons performance, and estmatng travel demand. An nnovatve methodology s presented n ths paper to estmate the daly O-D demand usng cellular probe trajectory nformaton. Tang advantages of the emergng cell-phone tracng technologes, the cellular probe trajectores are obtaned by recordng all the sgnal-transton events and perod locaton update events of cellular probes to determne the trp orgns and destnatons. To apply the O-D estmaton to a broader spectrum, the probablty of cell-phone ownershp was treated as a condtonal probablty dependng on users soco-economc factors avalable n the census data such as age, rage, household ncome, etc.. A mathematc model was desgned to convert the cellular counts nto equvalent vehcle counts, usng the posteror nformaton obtaned from the characterstcs of cellular probe trajectores. Next, the travelng populaton daly O-D demand was estmated va a robust Horvtz-Thompson estmator. Fnally, the methodology was tested va a VISSIM smulaton and results were compared wth a conventonal smple random samplng (SRS) method. The comparson outcome shows great potental of usng cellular probe trajectory nformaton as a means to estmatng daly O-D travel demand. Key words: Daly O-D demand estmaton, Cellular probe data, Cell-phone tracng technology, Horvtz-Thompson estmator TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

3 Zhang, Qn, Dong and Ran INTRODUCTION Wth respect to the ncreasng needs on the traffc demand forecastng, the estmaton and predcton of O-D matrx has become an mportant ssue n the current transportaton plannng and operaton scope. The O-D estmaton s the essental source for traffc demand nformaton. Generally, there are two types of the O-D estmaton methods. One s the survey-based O-D estmaton method, whch utlze the trp survey data to generate the O-D matrx (, ). The other one s the traffc-counts-based O-D estmaton method, whch uses the observed ln traffc counts to reversely derve the O-D matrx (-). Tradtonal survey-based trp dary approach to estmatng trp generaton and dstrbuton s tme-consumng and cost-prohbtve (, ). The estmaton may vary from one study as a result of the lmtaton of the survey sample sze and samplng randomness. The counts-based methods used the exstng traffc devces such as loop detectors and vdeo cameras to obtan the ln traffc counts. The O-D matrx s derved by an opposte way of traffc assgnment (). But the naturally most of the models are underdetermned (, ). In recent years, some postonng technologes such as GPS and cell phone emerged to be used to montor real-tme traffc status(, ), provde traveler nformaton (, ), and estmate travel demand (-). Wth the popularty of cell phone and emergng cell-phone tracng technologes, usng cellular probe data have the great potental to provde a larger sample sze n a tmely manner. Pan et al. () proposed a method to record the cell-phone postons every hours and aggregated them to obtan the trp dstrbuton between each O-D pars. Caceres () proposed another method to record the Locaton Updates (LU) events to count the O-D trp flows between each Locaton Area (LA) and convert the cell-phone counts nto vehcle counts. Sohn and Km () developed an dle Handoff (HO) technology for cell-phone postonng to get the vrtual traffc counts on observaton lns, and use the synthetc method to derve the tme-dependent O-D matrx from the ln traffc counts. There are three major lmtatons exstng n current lteratures. The frst one s the sgnal-transton events are not fully used. Snce the LA ncludes tens of cells, and ts coverage s much larger than cell, sometmes, the data fuson of the LU and HO events wll ncrease the complexty of the O-D estmaton problem. Most of lteratures use ether the HO events or the Locaton Update events (Includes perodc locaton update (PLU)) to determne the trajectores of cell phones or cell-phone counts. The lmtaton of usng only one type of transton events s that t only records a part of nformaton of cellular probe trajectores, n whch case t may lead to naccurate postonng results. The second one s that the soco-economc dfference of cell-phone owners s omtted. Consderng the cell-phone owner group as a sample selected from the populaton, naturally the sample can be treated as a smple random sample. Ths s the so-called Smple Random Samplng (SRS) strategy. Most of lteratures adopted ths method (,,, ). However, whether a person owns a cell phone depends on several mportant factors, such as age, household ncome, race etc.. Dsregardng the dfference among those factors may leads to soco-economc bas. The thrd one s that cell-phone counts are not properly converted nto vehcle counts. As TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

4 Zhang, Qn, Dong and Ran we now, aggregaton of the cellular probe trajectores wll return the cell-phone counts. However, n transportaton area, the nterests manly focus on the vehcle counts. Typcally, the cell-phone counts are not equal to vehcle counts, snce dfferent vehcles may carry dfferent number of cell-phone owners. It needs to be converted before t can be used. In current lteratures, ths problem s ether omtted (-, ), or treated by predefnng an equvalent factor to do the conversons (). Ths paper proposed a method tryng to cover the above three lmtatons. The method uses the full nformaton on the sgnal-transton events to produce cellular probe trajectores. Also the soco-economc factors are taen nto consderaton to generate the probablty of cell-phone ownershps. Then, the vehcle counts are aggregated by usng the characterstcs of the cellular probe trajectores. Ths paper s organzed as follows: The secton ntroduce the cell-phone tracng technology; The secton ntroduce the proposed method to estmate the daly O-D demand; The secton gves a smulaton based experment to demonstrate and verfy the proposed method; The last secton gves out the major concluson of ths paper CELL-PHONE TRACKING TECHNOLOGY The cell-phone tracng technology uses the sgnal transton between two contermnous cells to determne the locaton of the object (). Sgnal transton refers to a phenomenon that some parameters change ther values at some vrtual boundares of ts defned locaton regon. In practce, a cell sze and boundary changes wth tme due to the fluctuaton of sgnal coverage. Generally, n the GSM networ, the parameters whch can be used to trac the sgnal transtons are Locaton Area Code (LAC), servng cell ID (Cell ID) and Tmng Advance (TA). The correspondng sgnal-transton events n GSM networ are Locaton Update (LU) for LAC, HO for Cell ID and the transton of TA values, respectvely (). When a cell-phone wth an on-gong phone call crosses the boundary of dfferent cells, a HO operaton, n whch the cell d and the tme stamp are recorded automatcally by the system, wll be executed. If the cell phone s turned on but not on call, a LU event wll be automatcally recorded when t crosses the boundary of dfferent Locaton Areas (LA). The tmng advance s used to compensate for the tme that taes a wreless sgnal to travel at the speed of lght between a Base Transcever Staton (BTS) and the cell phone (). Multplyng TA and 0 meters can gve the mnmum dstance to a BTS. The maxmum dstance wll be (TA+) multplyng wth 0 m. Smlar to a HO, the tmng advance transton can only be collected when a cell phone s n on-call mode. In addton to the sgnal-transton events, the cellular system also provdes a perodc locaton update for the cell ID nformaton (). Generally, the cellular system wll update each cell phone s cell IDs perodcally and add t nto a Database. Here the locaton nformaton provded by ths event s the cell ID and tmestamp. Ths event s called Perodc Locaton Update (PLU), and the length of the perod can be adjusted by the moble carrer. Usually, the update perod s set to hours by default. Table. Typcal sgnal-transton events n Fgure. Events Area Tmestamp TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

5 Zhang, Qn, Dong and Ran PLU Cell 0:00 TA Cell 0: HO Cell > Cell 0: LU Cell > Cell 0: PLU Cell :00 PLU Cell :00 PLU Cell :00 PLU Cell :00 HO Cell > Cell :0 TA Cell : LU Cell > Cell : PLU Cell :00 PLU Cell 0:00 Combnng the above cellular locaton technologes, the cellular probe trajectores can be obtaned by recordng the sgnal-transton (HOs, LUs and TAs) and the PLU events. Fgure. gves an example to llustrate the process of cellular tracng method. Assume a cell phone starts travelng at Cell. Its trajectory can be traced by the sgnal transtons and the PLUs. Table. descrbes the dfferent events recorded by the system. TAZ TAZ LA LA Boundary LA TAZ TAZ Poston ponts TAZ Trajectory TAZ Fgure. Illustraton of cellular tracng technology The cellular tracng method provdes a possblty to record the Orgn-Destnaton nformaton by analyzng the trajectory of cell-phone users. Gur Y.J. et. al. () consdered the locaton of the frst sgnal transton event (mostly s the event that the frst tme turn on the cell phone n the mornng and regster to GSM networ) as the trp orgn. In ths paper, we adopted ths method to dentfy the trp orgns. The problem s how to decde the trp end. One possble TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

6 Zhang, Qn, Dong and Ran soluton s to consder the TAZs (Transportaton Analyss Zone) wth the longest dstance from the trp orgn and most PLUs recorded as the destnatons. Tang the Fgure. as an example, the trp starts at TAZ snce the frst events happens at TAZ. Accordng to Table., TAZ has the longest dstance and t has the longest duraton n a day. It s easy to conclude that TAZ s the trp end. TAZ Boundary TAZ TAZ Fgure. Illustraton of mperfectly overlappng between TAZs and cells Typcally, TAZs wll not match the boundares of cells perfectly. A cell may be covered by multple TAZs, meanwhle a TAZ may cover one or more cells entrely or just a part of a cell. As shown n Fgure., TAZ and TAZ cover the entre cell and cell respectvely, and share the cell and cell. If there s no sgnal transton event, the system can only tell the cell ID nformaton by the PLU events, whch may cause spatal errors because t s hard to determne whch TAZ the cell belongs to. Pan et al. () used a probablty of one cell belongng to a TAZ accordng to the proporton of area covered n each TAZ to determne t s covered by whch TAZ, f there s no addtonal demographcal nformaton provded. We adopted ths method n ths paper METHODOLOGY. Study Desgn The sgnal-transton events and PLUs assocated wth the correspondng cell-phone ds and tmestamps can be collected and stored n a database at the operatng center of the cellular carrer. It s easy to get a specfc cell-phone owner s trajectory by just dong a query n the database. The proposed method wll frst generate the ndvdual cellular probe trajectory, n whch the cell-phone sgnal transton and PLU events are recorded to form the trajectory. After the collecton of cellular probe trajectores, the dentfcaton of trp orgns and ends wll be executed. Then a vehcle-per-cellphone equvalent factor wll be calculated to covert the cell-phone trps nto vehcle trps, snce a vehcle may carry dfferent number of cell-phone owners. Tll now, what we got s the cellular trps and the correspondng equvalent vehcle trps. However, those trp maers who don t own cell phones should also be consdered. A data aggregaton process wll be carred out to project the sampled vehcle O-D matrx to the populaton vehcle O-D matrx. As a result, the actual O-D matrx can be obtaned followng TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

7 Zhang, Qn, Dong and Ran these above procedures. Fgure. shows the procedures of the O-D estmaton method. Collect the cellular probe data Generate cellular probe trajectores Purpose: Transform the cell phone sgnal transton and PLU events to cell phone trajectores Identfy the trp orgns and trp ends Purpose: Identfy the trp orgns and ends. If a cell s covered by multple TAZs, use Pan et al.() s method to determne the targeted TAZ. Calculate vehcle-cell-phone equvalent for each cellular probe Purpose: Convert the sampled cell phone trps nto sampled vehcular trps Data Aggregaton Purpose: project the sampled vehcular O-D matrx to the populaton O-D matrx Notatons: Fgure. Flow chart of the estmaton process p cp f f f - the condtonal probablty of cell-phone ownershp dependng on factors,,... n ( f, f,... f ) n Resulted O-D matrx p( cp f ) - the condtonal probablty on factor f n n p c m - the maret share of a specfc carrer m p( cp ) - the maret penetraton of cell phones f - the vehcle-per-cellphone equvalent factor vc f pvo - the average passenger-vehcle occupancy N - the total populaton n TAZ T - the O-D flows from TAZ to j T ˆ - the estmated value of T - the estmated value of T of SRS method S - the cell-phone owner group n TAZ T from cell-phone owner group of our method p - the posteror probablty of cell-phone ownershp for one or several carrers of the -th people n TAZ. It may vary n terms of ages, ncome and sex. TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

8 Zhang, Qn, Dong and Ran 0 0 Y - the ndcatng varable, f -th people n populaton has a trp between TAZ and j, otherwse 0. y - the ndcatng varable. f -th people n cell-phone owner group has a trp between TAZ and j, otherwse 0. P - the proporton of people have trps between TAZ and j P ˆ - the estmated value of P - the estmated value of. Important Assumptons P of SRS method P from cell-phone owner group Before ntroducng the daly O-D demand estmaton method, two mportant assumptons should be made n order to mae the cell-phone tracng method can be used to estmate the O-D demand between TAZ pars.. There mght be multple cellular carrers exstng n the research areas. Each of the carrers s operated ndependently. It means that the owner groups and the sgnal coverage of each cellular carrer are ndependent. In ths case, each cell-phone owner group whch belongs to a specfc cellular carrer can only be treated as ndvdual sample set.. The cell-phone ownershp pattern s dentcally dstrbuted among dfferent cellular carrers. That means dfferent cellular carrers have the same dstrbuton of ther owner s age, ncome, race etc.. Ths assumpton holds n the general condtons, although there are some cellular carrers havng dfferent dstrbuton n terms of the subscrber s demographcs, such as MetroPCS has a heavy emphass on prepad phone plans, Nextel had a strong busness focus. The frst assumpton guarantees the generaton of cellular probe trajectores and the dentfcaton of trp orgns and destnatons can be carred out ndependently among varous cellular carrers. After the trp orgns and destnatons are determned, the dfference on the sgnal coverage of dfferent carrers wll no longer nfluence the accuracy estmaton results. The second assumpton guarantees the generaton of the cell-phone ownershp probabltes can be appled to multple carrers.. Determne the Probablty of Cell-phone Ownershp In tradtonal trp survey methods, the SRS strategy are generally adopted to desgn the trp surveys, n whch at most % samplng rate are used to get the unbased estmaton of trps n a TAZ. But sometmes a lower samplng rate maes the samplng error ntolerable. The cellular probe data gves another way to aggregate the trp data because of ts unque advantages:. Cellular probe data s easy to be collected.. The sze of cell-phone owner group s much larger than the sample sze n tradtonal surveys. For example, n Unted States, the number of cell-phone users reaches approxmately % of the total populaton n 00 (), n whch the major cellular carrers add up to nearly 0% maret share (Verzon: %, AT&T: %, Sprnt: %) (0). Consderng the large sze of the TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

9 0 Zhang, Qn, Dong and Ran exstng cell-phone owner group, t would be clear that the samplng error should be substantally less than the tradtonal O-D surveys. It should be notced that although the cell phone maret penetraton rate reaches 0% of the maret share, n practce, snce the cellular probe data are collected ndependently among dfferent cellular carrers, t s more possble to collect the data from one or two cellular carrers. Therefore, we need to consder both the cell phone maret penetraton rate and the maret share of ndvdual cellular carrers. Many researches treated the cellular probe trajectory data as the SRS survey data. Each ndvdual n the sample s chosen randomly and entrely by chance, such that each ndvdual has the same probablty of beng chosen at any stage durng the samplng process. In other words, each ndvdual has the same probablty to own a cell phone. Here the probablty of owng a cell phone s a pror probablty and equals to the cell-phone maret penetraton rate. However, the maret penetraton rate s a nd of pror probablty whch s obtaned from some maret research reports or papers. It may lead to naccuracy f dsregardng the possble socal-economcal bas. Typcally, the probablty of whether a person owns cell phones should be related to many factors, such as age, ncome and race, etc. (). For example, young people consst of the largest group of the cell-phone owners n terms of the cell-phone owners age dstrbuton. Therefore, the young people wll have larger probablty to own cell phones than the old ones. And n some cases, the hgher ncome people wll have larger probablty to own cell phones. The condtonal probablty of cell-phone ownershp can be assumed to have the followng lnear relatonshp: p cp f, f,... f p( cp f ) p( cp f )... p( cp f ) () n n n where,..., n s the coeffcents where n. Generally, equaton () needs to be 0 calbrated to determne the coeffcents. In many stuatons, the followng equaton s used to calculate the probablty p( cp f ) : n n p cp, f p f cp p cp n p ( cp f ) n p f P f n Consderng the stuaton for a specfc cellular carrer m, the probablty of a person owns a cell phone n TAZ turns to be:,,... ( ) ( )... ( ) cm n cm n n p p p cp f f f p p cp f p cp f p cp f () If multple carrer data are avalable, the equaton () turns to be: M n n cm m ( ) ( )... ( ) () p p cp f p cp f p cp f p where M s number of cellular carrers from whch the data are obtaned. Note that n TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

10 0 0 Zhang, Qn, Dong and Ran In practce, due to the prvacy concerns, most of the personal nformaton requred for the equatons ( ) cannot be obtaned drectly from cellular carrers or operators. However, the U.S. census provdes a large amount of demographc survey data for us to produce the dstrbutons of the personal nformaton (age, ncome, race, etc.). We can utlze the nformaton to calculate the probablty of cell-phone ownershp. The case study part wll gve a detaled procedure to determne the cell-phone ownershp probabltes.. Vehcle-per-cellphone equvalent factor Typcally, the cell-phone tracng technology wll return the cellular probe counts. However, n transportaton plannng feld, the man nterest s on vehcle flows rather than the cellular probe flows. Consequently, a vehcle-per-cellphone equvalent factor f wll be used n our method vc to convert cellular probe flows nto equvalent vehcle flows (). We desgned a method to estmate the f based on the posteror nformaton obtaned from the characterstcs of the vc cellular probe trajectores. Accordng to the cellular probe trajectory characterstcs, the set of trajectores can be dvded nto three subsets:. The set of trajectores crossng at least two LA boundares,.. The set of trajectores crossng just one LA boundares,.. The set of trajectores wthout crossng any LA boundares,. For the frst two subsets of trajectores, here are three assumptons:. Phones n close proxmty (.e. the same car) generate sgnal transton events at exactly the same tme. In practce, ths assumpton needs to be relaxed snce phone varaton s qute hgh and sgnal events may have qute large dfferences n tmng even for phones n the same car. The followng two assumptons hold based on ths assumpton.. There cannot be two vehcles crossng two contnuous LA boundares at same tmestamps. Typcally, the dmenson of a LA s - mles by - mles. There s a very small possblty that some parallel travellng cars crossng at least two LA boundares at two same tmestamps. If two cellular probe trajectores crossng two contnuous LA boundares at two tmestamps t and t, they should be n the same vehcle.. Wthn the saturaton headway, there s only one vehcle crossng LA boundares n each lane. The default saturaton headway s.0 seconds. Wthn two tmestamps t and t, there s only one vehcle crossng LA boundares n each lane. The estmaton of f for the trps crossng at least two boundares wll be based on the cpv frst assumpton. Assumng a set of cellular probe trajectores s,...,... m crossng at two LA boundares at tmestamps t and t, so the expected value of the number of passengers n wll be: s s () p s The average passenger-vehcle occupancy f (passengers per vehcle) () s appled to pvo determne the number of vehcles crossng the two LA boundares at tmestamp t and t : TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

11 Zhang, Qn, Dong and Ran Vehs s s f pvo So the vehcle-per-cellphone equvalent factor for cell-phone owner n set s: s f vc s s f pvo, s s For the second subset of the trps, the thrd assumpton s used. Suppose a cell-phone owner n set crosses a LA boundary at tmestamp t. There are lns located at the boundary. Each of the ln j has several lanes. The number of average occuped lanes (the average number of lanes whch are occuped by vehcles) at ln durng pea hour s. A set j of cell phones crossng the boundary between tme t and t t. Note that conssts of t both the cell phones crossng only one LA boundary and those crossng at least two LA boundares at tme t and t. So the vehcle-per-cellphone equvalent factor for set wll be: f vc j j t t t f pvo, () For the thrd subset of cellular probe trajectores, the average value of subsets s assgned to them: f of the frst two vc f vc j f vc j j f j vc, () 0 where the operator means that the sze of the set.. Trp Generaton and Dstrbuton The trp generaton and dstrbuton are the frst two steps n the tradtonal four-step transportaton plannng process. The trp generaton s to decde the number of trps whch are produced or attracted n a specfc TAZ. The trp dstrbuton process s to dstrbute the productons and attractons predcted by trp generaton model to the O-D flows from each producton zone to each attracton zone j. Due to the lmtatons on the sample szes of surveys, the tradtonal trp generaton and dstrbuton model cannot secure an accurate result. The cell-phone tracng technology provdes a larger sample. Here we ntroduce a new method to obtan the populaton O-D demand combnng trp generaton and dstrbuton together. TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

12 Zhang, Qn, Dong and Ran For the total populaton, the proporton of people who have trps between TAZ and j should be: N N P Y Y To get the value of T, t only needs to multply P wth N : N T Y N P If treatng the cell-phone owner group as a smple random sample. The samplng results can drectly be estmated by the followng equaton: Pˆ n y S Note that n SRS method, the sze of cell-phone owner group can be estmated by: S Np ( cp ) p c m So the estmated value of T n SRS survey method s: Tˆ N Pˆ n y p ( cp ) p cm () Snce the dstrbuton of cell-phone owners cannot be consdered as the smple random sample, the T ˆ cannot be nferred drectly usng equaton (). A Horvtz Thompson (HT) estmator () of the P s proposed: P y () S Np From equaton (), t can be seen that the hgher probablty of ownng cell phones, the less weght the correspondng y s gven, n ths way the HT estmator uses probablty to weght the responses n the estmatng the total. The HT estmator of T can be defned as follows: 0 T y NP S p () TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

13 Zhang, Qn, Dong and Ran Note that T s the O-D trps between TAZ and j, but what we need s the vehcle O-D flows. So the vehcle-per-cellphone factor should be added n the estmator: T Veh S p vc y f () Now to prove the HT estmator of P s an unbased estmator. Let f S, that s to say the th ppl has cell phone n TAZ 0 Otherwse Then the estmator P can be expressed n followng form: P N Y Np The expectaton of P s: N N N Y Y E Y p () E P E Y P Np N p N p The estmator P s the unbased estmator of P. Furthermore, the varance of the estmator P s. N N N Y Y Var Y Y C ov(, ) m m () N p N p m p p m Var P Var Note that and Var E E p ( p ) m m m m m Cov(, ) E E E p p p where p s the jont probablty of both the m th people and the m th people own cell phones. Consderng two people n sample have an ndependent probablty to own cell phones, the TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

14 equaton () turns to be: Zhang, Qn, Dong and Ran N N ( ) N Y Y p p Y ( p ) () N p N p N p Var P Var If assume the people n analyzed TAZ have the same probablty p of cell-phone ownershp, the expected value of varance turns to be: N ( p) ( ) ( ) p p P E Var P E Y E P N p N p N p () Then the expected value of standard devaton should be: ( p ) P ( p ) P E SD P E N p N p (). CASE STUDY SIMULATION EXPERIMENTS (a) TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

15 Populaton Zhang, Qn, Dong and Ran (b) Fgure. (a) Cell tower locaton map of the research area (b) Correspondng smulaton networ Ths smulaton ams to provde a verfcaton of the proposed O-D estmaton method. The proposed research area s Dane county n the southwest of the state of Wsconsn. To be smplfed, t s dvded nto TAZs. Fgure. (a) shows the cell-phone tower locatons and Fgure. (b) shows the correspondng VISSIM smulaton layout of the research area. The red crcles n Fgure. (b) are the ntersectons of lns and LA boundares.. x Populaton dstrbuton by age (US Census 00) Age (years) Age (a) Independent Varables (b) Cell-phone sample TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

16 0 Income - 0 % - % up % Less than $0,000 % $0,000 up % Don t now/refused % Zhang, Qn, Dong and Ran (c) Fgure. (a) U.S. census data of age dstrbuton, 00 () (b) U.S. census data of ncome dstrbuton, 00 () (c) Demographc nformaton on cell-phone ownershp pattern () The nput data nvolve wth nput modules: the trp survey data module, the cell phone ownershp dstrbuton module and the vehcle occupancy dstrbuton module. The smulaton perod s set to be hours to estmate the daly O-D demand data. The nput modules prepared the nput parameters as well as the nput O-D matrx to start the VISSIM smulator. A cell phone sgnal transton events module wll be pared wth the VISSIM smulator module to provde the random events such as call-n and call-out events, whch can be used to generate the HO events. The trp survey data module uses the Wsconsn State-wde Trp survey data () as the aggregated nput daly O-D matrx. Also the trp survey data contans the age and household ncome nformaton whch can be used n the cell phone ownershp dstrbuton module. The cell phone ownershp dstrbuton module s desgned to assgn the cell phone to each trp maer wth cell phone ownershp probabltes. To smplfy the demonstraton, only the ncome and age are taen nto consderaton for the cell-phone ownershp probablty. Fgure. (a) and (b) llustrate the U.S. census demographc data for the populaton by age and ncome. Fgure. (c) shows the populaton age and ncome dstrbuton, from whch t s easy to get the condtonal probablty p( cp age ) and p( cp ncome ). To get the value of p( cp age ) and p( cp ncome ), t can be calculated as followng: P age p cp, age p age cp p cp p ( cp age) p age p ncom e p cp, ncom e p ncom e cp * p cp p ( cp ncom e) p ncom e where p cp s the maret penetraton rate of cell phones. In ths smulaton, t s set to be 0., and the maret share of a specfc carrer s set to be 0.. Use the equaton () to determne the probablty of cell-phone ownershp: p cp age, ncom e p ( cp age) p ( cp ncom e) where s the coeffcent between 0 and. In ths smulaton, t s set to be 0.. In 00 U.S. census data (), Dane county has a,0 resdents. The cell-phone TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

17 0 Zhang, Qn, Dong and Ran ownershp probablty for each people s generated based on the above demographc nformaton. Then the cell-phone owners are assgned to each ndvdual vehcle. The vehcle occupancy dstrbuton module s to generate the random numbers of passengers assgned to each ndvdual vehcle. It s used to convert the trp counts nto vehcle counts. The average Passenger-Vehcle Occupancy n Unted States s. (). A [,] dscrete unform dstrbuton s used to generate the random numbers. The VISSIM smulaton tool s employed to smulate the vehcle movements between each O-D par. The nput O-D table s assgned by VISSIM s bult-n Dynamc Traffc Assgnment (DTA) algorthm to generate the vehcle flows on lns. The centers and boundares of cells and LAs are predefned wthout any tme-dependent fluctuatons n the smulaton networ. The radus of cell coverage s set to 00 ft. The boundares n VISSIM are set as data collecton ponts on lns where the cell or LA boundares ntersect wth. The data collecton ponts can record each vehcle s ID and tmestamp when the vehcle crosses them. In ths smulaton, the cell phones are assumed to be set n turn-on mode automatcally. Durng each smulaton tme step, the system wll chec whether there s any sgnal-transton event happened. The cell phones are assgned wth a small probablty to determne the occurrence of call-n and call-out events. The duratons are determned by assgned a random number. The HO events wll be recorded when the cell phones are n on-call mode and cross the data collecton pont at cell boundares. The TA events wll be record wth ts correspondng cell centers when cell phones are n on-call mode. The LU events wll be record when cell phones cross the data collecton ponts at LA boundares. The PLU events wll be recorded every two hours wth ts correspondng cell centers as well. After collectng the cellular probe trajectores, the O-D estmaton ntroduced n Fgure. s employed to get the estmated O-D matrx. The smulaton process s shown n Fgure.. Tme: T Cell phone ownershp dstrbuton Trp Survey Results Passenger occupancy dstrbuton For each vehcle For each cell phone Smulaton Input: O-D table Sgnal Transton? Generate sgnal tanston events VISSIM Smulator Store the event Y N Generate Cell phone trajectores Next phone Next vehcle O-D estmaton Fgure. Illustraton of the smulaton process Tme update: T = T + TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

18 Zhang, Qn, Dong and Ran The SRS method s also mplemented n the smulaton, and the average passenger-vehcle occupancy s used to convert the populaton trps nto vehcle trps. The results are shown n Table.. It can be found that most of the estmated O-D flows have less percentage error than the SRS method. The average percentage error of the proposed method s.%, whle the SRS method returns.%. Snce the cell phone user group s not naturally a random sample, the HT estmator can gve a more accurate estmaton results comparng to SRS method. Moreover, our method uses the vehcle-per-cellphone factor to convert the cell phone counts nto vehcle counts, whle the SRS method employs the pror Passenger-Vehcle Occupancy nformaton. The smulaton results fully show the advantage of our method over SRS method. Table. Smulaton results of proposed method and SRS method O-D Par Org. O-D Est. O-D Per. Error SRS O-D Per. Error ->.% 0.% -> 0.%.% -> 0.%.% -> 0.%.% ->.%.0% ->.0% 0.0% ->.%.0% ->.%.% ->.0%.0% ->.%.% -> 0.% 00.% ->.% 00.% -> 0.% 0.% -> 00.00% 00.% ->.% 0.% ->.0%.0% -> 0.%.% ->.0% 0.0% -> 0.%.0% ->.% 0.0% -> 0.%.% ->.%.% -> 0 0.%.% -> 0 0.%.% ->.%.0% Furthermore, the estmated O-D volumes versus orgnal O-D volumes are plotted n Fgure. (a) and (b). It can be seen that both the results from the proposed method and SRS method have strong relatonshp wth the orgnal O-D flow. The regresson shows both the lnes fts the data very well, n whch the coeffcents of determnaton R of our method are 0. and 0., respectvely. To better llustrate the advantages of the proposed method, a senstvty analyss s carred TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

19 Percentage error Standard devaton Orgnal O-D Volume (veh) Orgnal O-D Volume (veh) Zhang, Qn, Dong and Ran out to see the nfluence of the cell-phone owner group sze (maret share of cellular carrers). The cell-phone maret penetraton rate s fxed at 0.. The maret share of cellular carrers s ncreased from 0. to. Note that here the maret share of cellular carrers s the total maret share of the carrers whch are avalable to provde cellular data. Fgure. (c) and (d) show the comparson between our method and SRS method n term of the percentage error and standard devaton of P wth the ncreasng of maret share of cellular carrers. It can be seen that the percentage error eeps unchanged at about % wth ncreasng of cellular carrers maret share. On the other hand, the percentage error of SRS method decreases untl the maret share ncreased to 0.. x x. New O-D VS. Org. O-D New OD = 0. * Org. OD +.. SRS. O-D VS. Org. O-D Org. O-D = 0. * SRS. O-D +.. R = 0.. R = Estmated O-D Volume of New Method (veh) x (a) SRS. Estmaton O-D Volume (veh) x (b) 0. New method 0. Our method 0. SRS method 0. RSS method Maret share of cellular carrers (P(cp) = 0.) Maret penetraton of cellular carrers (p(cp)=0.) (c) (d) Fgure. (a) Estmated O-D VS. Orgnal O-D (b) RSS O-D VS. Orgnal O-D (c) Maret penetraton rate VS. Percentage error (d) Maret penetraton rate VS. Standard devaton In Fgure. (c) and (d), the standard devaton of our method eeps unchanged below % wth the ncreasng of maret share, whle the SRS method wll decrease from more than % to % when the maret share ncreases from 0. to. TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

20 Zhang, Qn, Dong and Ran Both the results of percentage error and standard devaton show the proposed method s robust method for the daly O-D matrx estmaton. Generally, the smaller maret share of the cellular carrers n practce, the less cellular trps can be obtaned from the trajectores. Then the accuracy of estmaton results wll be more dffcult to attan. Dfferent wth the SRS method, the proposed method can stll eep good performance at smaller data set CONCLUSIONS AND FUTURE RESEARCH EXTENSION Tradtonal survey-based trp dary approach to estmatng trp generaton and dstrbuton s tme-consumng and cost-prohbtve. The estmaton may vary from one study as a result of the lmtaton of the survey sample sze and samplng randomness. Wth the popularty of cell phone and emergng cellular tracng technologes, usng cellular probe data have the great potental to provde a larger sample sze n a tmely manner. In ths paper, an exploratory methodology was presented to estmate the daly O-D demand usng cellular probe trajectores. They can be obtaned by tracng all the sgnal-transton and perodc locaton update events of cellular probes to determne the trp orgns and destnatons. To overcome the potental soco-economc bas, a condtonal probablty of cell-phone ownershp was estmated usng traveler s soco-economc factors that are readly avalable n the census data. Then, a vehcle-per-cellphone equvalent factor was generated based on the posteror nformaton of the characterstcs of cellular probe trajectores. In other words, ndvdual cellular trps were converted nto equvalent vehcle trps. Next, the trp generaton and dstrbuton were obtaned smultaneously usng a Horvtz-Thompson estmator so that the populaton O-D demand can be estmated. The Horvtz-Thompson estmator was proved to be an unbased estmator of the populaton O-D demand n theory. A VISSIM based smulaton was desgned to exemplfy the proposed method. A smple random samplng (SRS) method, the prevalng method n current lterature, was also smulated. The comparson between the outcome of cellular probe data and SRS shows that both methods yelded desrable goodness-of-ft n terms of R but the average percentage error of SRS s almost twce of the cellular probe data method, demonstratng the superorty of the proposed methodology. The senstvty analyss has also shown that the proposed method provdes a robust estmaton for the daly O-D matrx. To verfy the valdty of the assumptons of proposed methodology, a feld test s needed n the future study, n whch the cellular probe data and cell boundares wll be obtaned from cellular carrers. A method should be proposed to elmnate the estmaton error caused by varatons of cell szes and boundares. A more accurate method to determne the trp orgns and destnatons should be developed. And an addtonal survey s needed to get accurate demographc nformaton of cell-phone owners. An exstng O-D demand matrx wll be used as the ground truth to verfy the correctness of the estmaton results. TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

21 Zhang, Qn, Dong and Ran REFERENCE. Meyer, M.D. and E.J. Mller, Transportaton Plannng: A Decson-Orented Approach. McGraw-Hll Boo Company, INC, New Yor, NY.. Gamo, G.T., Modfcatons To Tradtonal External Trp Models. 00. pp. p. -.. Abrahamsson, T., Estmaton of Orgn-Destnaton Matrces Usng Traffc Counts - A Lterature Survey. INTERIM Report... Sheral, H.D. and T. Par, Estmaton of Dynamc Orgn-Destnaton Trp Tables for A General Networ. Transportaton Research Part B: Methodologcal, (). 00. pp. -.. Wong, S.C., et al., Estmaton of Multclass Orgn-Destnaton Matrces from Traffc Counts. Journal of Urban Plannng and Development, (). 00. pp. -.. Stopher, P.R. and S.P. Greaves, Household Travel Surveys: Where Are We Gong? Transportaton Research Part A: Polcy and Practce, (). 00. pp. -.. Hazelton, M.L., Some Comments on Orgn-Destnaton Matrx Estmaton. Transportaton Research Part A: Polcy and Practce, (). 00. pp. -.. Qu, Z., et al. State of the Art and Practce: Cellular Probe Technology Appled n Advanced Traveler Informaton Systems. In Transportaton Research Board th Annual Meetng. Washngton D.C.: Transportaton Research Board Astarta, V., et al., Motorway Traffc Parameter Estmaton from Moble Phone Counts. European Journal of Operatonal Research, (). 00. pp. -.. Caceres, N., J.P. Wdeberg, and F.G. Bentez, Revew of Traffc Data Estmatons Extracted from Cellular Networs. Intellgent Transport Systems, IET, (). 00. pp. -.. Asaura, Y. and T. Iryo, Analyss of Tourst Behavour based on the Tracng Data Collected usng a Moble Communcaton Instrument. Transportaton Research Part A: Polcy and Practce, (). 00. pp Pan, C., et al., Cellular-Based Data-Extractng Method for Trp Dstrbuton. Transportaton Research Record: Journal of the Transportaton Research Board. 00. pp. pp -.. Caceres, N., J.P. Wdeberg, and F.G. Bentez, Dervng Orgn Destnaton Data from A Moble Phone Networ. Intellgent Transport Systems, IET, (). 00. pp. -.. Keemn, S. and K. Daehyun, Dynamc Orgn-Destnaton Flow Estmaton Usng Cellular Communcaton System. Vehcular Technology, IEEE Transactons on, (). 00. pp Whte, J. and I. Wells. Extractng Orgn Destnaton Informaton from Moble Phone Data. In Road Transport Informaton and Control, 00. Eleventh Internatonal Conference on (Conf. Publ. No. ) Lu, J., et al. Applyng Cellular-Based Locaton Data to Urban Transportaton Plannng. In Applcatons of Advanced Technology n Transportaton. Chcago: ASCE Mrcea, I., S. Eml, and H. Smona. Cell ID Postonng Method for Vrtual Tour Gudes Travel Servces. In ECAI 00 - Internatonal Conference. Ptest, Romana: Electroncs, Computers and Artfcal Intellgence Gur, Y.J., S. Behor, and C. Solomon. An Aggregate Natonal Transportaton Plannng Process n Israel: Formulaton and Development. In Transportaton Research Board th Annual Meetng. Washngton D.C.: Transportaton Research Board Bacground on CTIA's Sem-Annual Wreless Industry Survey. 00; Avalable from: fles.cta.org/pdf/ctia_survey_year_end_00_graphcs.pdf. 0. US Wreless Data Maret Update - Q. Chetan Sharma Consultng Co. Ltd Cell Phone Naton 00. Marst Insttute for Publc Opnon Gan, A. and K. Lu, Vehcle Occupancy Trends n Florda: Evdence from Traffc Accdent Records. Transportaton Research Board th Annual Meetng. Transportaton Research Board. pp. p. 00. Konn, H.S., Statstcal Theory of Sample Survey Desgn and Analyss. Amercan Elsever Publshng Company, INC., New Yor, NY.. Age and Sex Dstrbuton n 00. U.S. Census Bureau Annual Socal and Economc Supplement 00. U.S. Census Bureau. 00. TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.

22 Zhang, Qn, Dong and Ran. Statstcs, B.o.T. NHTS/NPTS Database. 00; Avalable from: Statstcs, B.o.T., NHTS 00 Hghlghts Report. U.S Department of Transportaton, Washngton, DC TRB 0 Annual Meetng CD-ROM Paper revsed from orgnal submttal.